Non Locality

The discovery by John Bell in 1964 that nature is nonlocal is arguably one of the most dramatic in physics. Yet, surprisingly enough, and with very few notable exceptions, it was largely ignored by the physics community for a long time. When I first became interested in the subject, almost three decades after Bell’s result, I was shocked to realise that even the most fundamental questions about this phenomenon had not been asked. First and foremost, which states have nonlocal properties? All that was known was that a few particular states, such as the singlet state of two spin ½ particles, are nonlocal. But is nonlocality a generic feature of quantum mechanics, or do only a few, very exceptional states have this property? My first work on nonlocality was to raise, and answer, this question. In [1] (references refer to the list of best 20 papers), in collaboration with Rohrlich, and simultaneously and independently from Gisin, I showed that nonlocality is generic: Almost every quantum state, more precisely every entangled pure state of two or more particles separated in space, is nonlocal. This paper established nonlocality as a central, if not the central, aspect of quantum mechanics. This result is now viewed as so basic and so much part of the ABC of the subject, that entanglement and nonlocality are very often taken to mean the same thing, and these early papers are barely cited anymore!

After establishing that non-locality is a generic qualitative feature of quantum states, the natural question was to ask whether there is also a quantitative aspect: Are some states more non-local than others? In collaboration with Bennett et al., I established the quantitative description of nonlocality and entanglement. We introduced the concept of non-locality manipulation by local operations and classical communication in particular entanglement concentration and dilution [7] and entanglement purification [6]. We showed that different non-local states can be inter-converted from one to another by means of purely local actions and classical communication; states which can be converted into each other by such procedures must contain the same amount of non-locality [6,7,9]. This allowed us to introduce a natural quantitative measure of non-locality. (The unit of quantum non-locality derived in these papers is now customarily called the e-bit, i.e. a bit-of-entanglement, and it is the non-local counterpart of the well-known unit of information, the bit.) These papers constitute the basis of the modern view of non-locality and entanglement, namely non-locality (entanglement) as a resource which, very much like energy, can be stored, transformed from one form into another, and consumed for performing useful tasks.

In 1993, in a pioneering paper, Bennett and collaborators described a communication method they called teleportation. In this process the information contained in a quantum state is first disassembled into a purely classical part, that is communicated to the receiver by ordinary means (such as a telephone), and a purely quantum part that is teleported: information instantaneously jumps from the transmitter to the receiver without being anywhere in between. At present, teleportation is considered to be the paradigmatic quantum communication method. The experimental verification of this phenomenon posed very difficult challenges. I proposed a simplified quantum optical scheme that succeeded in avoiding the main difficulties. This led us [10] to the first experimental realisation of teleportation, arguably one of the best known experiments in quantum information.

Returning to the theory of entanglement, I mention two immediate applications of entanglement manipulation. In [6] we used the idea of entanglement distillation to design the first quantum error correction code for communication, i.e. a method to transmit faithfully quantum signals over noisy channels. In [8], in collaboration with Deutsch et al, I invented quantum privacy amplification, a new cryptographic protocol, and used it to obtain the first proof of absolute security of quantum cryptography in real settings. (All previous proofs were valid for only ideal, completely noiseless channels.) Work with Bennett et al. established the framework for describing multi-partite entanglement and showed that there are irreducible types of entanglement that cannot be converted one into the other in reversible ways. In [15], with Groisman and Winter, I provided the first operational meaning of the concept of quantum mutual information. In [3] I showed that the whole notion of nonlocality needed to be revisited – the nonlocality revealed by violations of Bell Inequalities is qualitatively different from that employed for teleportation. Paper [5] introduced the notion of “hidden” nonlocality, extending for the first time the scope of Bell inequalities beyond ideal von Neumann measurements. Finally, the Collins-Gisin-Linden-Massar-Popescu Bell inequality [14] was the first generalisation of the standard Clauser-Horne-Shimony-Holt inequality to arbitrary dimensions and is now recognised as the Bell inequality to use in the bipartite case.

That nonlocality can exist at all, given the constraints imposed by relativistic causality, is an extraordinary fact. To understand it better, together with Rohrlich, I asked whether the nonlocality originating from quantum mechanics is the only possible form of nonlocality [2]. Surprisingly, we found that even stronger nonlocal correlations are possible in principle, without contradicting relativity. The correlations we discovered are now considered to be the basic unit of nonlocality and are known as Popescu-Rohrlich correlations (or PR boxes). Whether or not such correlations exist in nature is an open experimental question. If they exist, quantum mechanics is wrong and has to be replaced. If they do not exist - why not? What is the fundamental physical principle that forbids them? These questions initiated an entire new field of research, one of the most active in present day quantum information.